# Nonlinear stability of a quadratic functional equation with complex involution

## Reza Saadati and Ghadir Sadeghi

Address:

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Faculty of Mathematics and Computer Sciences, Sabzevar Tarbiat Moallem University, Sabzevar, Iran

E-mail:

rsaadati@eml.cc

ghadir54@yahoo.com

Abstract: Let $X, Y$ be complex vector spaces. Recently, Park and Th.M. Rassias showed that if a mapping $f : X \rightarrow Y$ satisfies
\begin{eqnarray} f(x+i y)+ f(x-iy) = 2 f(x) - 2f(y) \end{eqnarray}
for all $x$, $y\in X$, then the mapping $f \colon X \rightarrow Y$ satisfies $f(x+y) + f(x-y) = 2 f(x) + 2 f(y)$ for all $x$, $y \in X$. Furthermore, they proved the generalized Hyers-Ulam stability of the functional equation () in complex Banach spaces. In this paper, we will adopt the idea of Park and Th. M. Rassias to prove the stability of a quadratic functional equation with complex involution via fixed point method.

AMSclassification: primary 39B72; secondary 47H10.

Keywords: quadratic mapping, fixed point, quadratic functional equation, generalized Hyers-Ulam stability.